First, lets focus on finding out the other two legs of the large triangle.
To do this, we use Pythagoras' Theorem.
So the left leg = √(16² + x²)
So the right leg = √(9² + x²)
Notice, the larger triangle is also a right angled triangle, that means the sum of the two legs squared = hypotenuse squared.
Since we have just worked out the two legs, we can substitute them into:
a² + b² = c²
(√(16² + x²) )² + (√(9² + x²) )² = (16 + 9)²
Notice that the power of two cancels out with the squareroots so we get:
(16² + x² ) + (9² + x² ) = (25)² (simplify and collect like terms)
256 + x² + 81 + x² = 625
337 + 2x² = 625 (subtract 337 from both sides to isolate the x )
2x² = 288 (divide both sides by 2)
x² = 144 (square root both sides)
x = √144
x = 12
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Answer:
x = 12
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Note: if you have any questions, please ask and I will be more than happy to help and give further explanations!